login
E.g.f. satisfies A(x) = exp(x^3 + x * A(x)).
3

%I #21 Feb 16 2025 08:34:05

%S 1,1,3,22,173,1836,24847,403474,7667865,167097016,4108985531,

%T 112562882334,3399748630357,112246652293972,4022094151907847,

%U 155461592488721866,6447531477912609713,285606134199075271536,13458367778796518816755

%N E.g.f. satisfies A(x) = exp(x^3 + x * A(x)).

%H Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/LambertW-Function.html">Lambert W-Function</a>.

%F E.g.f.: -LambertW(-x * exp(x^3)) / x = exp( x^3 - LambertW(-x*exp(x^3)) ).

%F a(n) = n! * Sum_{k=0..floor(n/3)} (n-3*k+1)^(n-2*k-1) / (k! * (n-3*k)!).

%o (PARI) my(N=20, x='x+O('x^N)); Vec(serlaplace(exp(x^3-lambertw(-x*exp(x^3)))))

%Y Cf. A349562, A362690.

%Y Cf. A362737.

%K nonn,changed

%O 0,3

%A _Seiichi Manyama_, May 01 2023